Well-Posedness of the Schrödinger -- Intermediate Long Wave system

The system coupled by the Schrödinger equation and the Intermediate Long Wave (ILW) equation is a particular model describing the interaction of long and short waves. We prove local and global well-posedness of the initial value problem associated with this system in Sobolev spaces of low regularity. Our approach relies on the use of energy estimates, Bourgain spaces, and Tao’s gauge transformation.